WASHINGTON — The primary victory of a tea party-blessed candidate in Indiana illustrates how closely Republican hopes for a majority in the Senate are tied to candidates who pledge to infuse the chamber with the deep-seated conservatism that has been the hallmark of the House since the Republicans gained control in 2010.

Richard E. Mourdock, who last week defeated Sen. Richard G. Lugar, a six-term incumbent, promises to bring an uncompromising ideology to Capitol Hill if he prevails in November. And he is not the only Senate candidate who contends that Senate Republicans are badly in need of new blood.

In Arizona, Missouri, Nebraska and Texas, Republican Senate candidates are vying for the mantle of tea party outsider. A number of them say that they would seek to press an agenda that is generally to the right of the minority leader, Sen. Mitch McConnell of Kentucky, and that they would demand a deeper policy role for the Senate's growing circle of staunch conservatives.

Some say they have not decided whether they would support McConnell, who could find himself contending with the type of fractious rank and file that has vexed the House speaker, John A. Boehner of Ohio.

More Information

"We need to shake up the Republicans," said Sarah Steelman, the Missouri state treasurer, who is seeking her party's nomination to run against Sen. Claire McCaskill, a Democrat.

Asked if that meant new leadership in the Senate, Steelman replied, "Possibly."

McConnell's leadership does not appear to be in jeopardy. Aides to McConnell say he has already secured enough votes for his re-election as leader, regardless of the November results. And supporters say such threats have surfaced in the past, only to fizzle after Election Day.

Republican hopefuls want the Senate to act more like the house. Dan Liljenquist, a tea party-backed Republican challenging Sen. Orrin G. Hatch in Utah's Primary next month, said Republican leaders in the House, many of them young upstarts themselves, ditched traditional rules of seniority last year and let energetic up-and-comers take on powerful roles.

In the Senate, Liljenquist said, "The leaders most anxious to take on the entitlement system and the entrenched problems the nation faces are being benched by a system that puts them at the bottom rung."